TRS Standard pair #516967135

details

property	value
status	complete
benchmark	#4.30c.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n063.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.87735509872 seconds
cpu usage	14.205027564
max memory	6.41486848E8

stage attributes

key	value
output-size	42481
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 2 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) NonInfProof [EQUIVALENT, 73 ms]
        (27) QDP
        (28) TransformationProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) DependencyGraphProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) TransformationProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) DependencyGraphProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) TransformationProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) DependencyGraphProof [EQUIVALENT, 0 ms]
        (39) AND
            (40) QDP
                (41) TransformationProof [EQUIVALENT, 0 ms]
                (42) QDP
                (43) QDPOrderProof [EQUIVALENT, 13 ms]
                (44) QDP
                (45) DependencyGraphProof [EQUIVALENT, 0 ms]
                (46) TRUE
            (47) QDP
                (48) UsableRulesProof [EQUIVALENT, 0 ms]
                (49) QDP
                (50) QReductionProof [EQUIVALENT, 0 ms]
                (51) QDP
                (52) TransformationProof [EQUIVALENT, 0 ms]
                (53) QDP
                (54) UsableRulesProof [EQUIVALENT, 0 ms]
                (55) QDP
                (56) QReductionProof [EQUIVALENT, 0 ms]
                (57) QDP
                (58) TransformationProof [EQUIVALENT, 0 ms]
                (59) QDP
                (60) UsableRulesProof [EQUIVALENT, 0 ms]
                (61) QDP
                (62) QReductionProof [EQUIVALENT, 0 ms]
                (63) QDP
                (64) TransformationProof [EQUIVALENT, 0 ms]
                (65) QDP
                (66) TransformationProof [EQUIVALENT, 0 ms]
                (67) QDP
                (68) QDPSizeChangeProof [EQUIVALENT, 0 ms]
                (69) YES


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   le(0, y) -> true
   le(s(x), 0) -> false
   le(s(x), s(y)) -> le(x, y)
   pred(s(x)) -> x
   minus(x, 0) -> x
   minus(x, s(y)) -> pred(minus(x, y))
   gcd(0, y) -> y
   gcd(s(x), 0) -> s(x)

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